Age in years 10 - 14 15 - 19 20 - 24 25 - 29 30 - 34 Frequency 6 8 14 10 12 In which group is the upper quartile?

Answer Details

To find the upper quartile, we need to first calculate the median, which is the value separating the higher half from the lower half of the data. To do that, we can use the formula: Median = ((n + 1) / 2)th term where n is the total number of data points. In this case, n = 6 + 8 + 14 + 10 + 12 = 50. Median = ((50 + 1) / 2)th term Median = 25.5th term Since we have an even number of data points, the median is the average of the two middle terms, which are the 25th and 26th terms when the data is arranged in order. To find these terms, we can use the cumulative frequency distribution: 10-14: 6 15-19: 6 + 8 = 14 20-24: 14 + 14 = 28 25-29: 28 + 10 = 38 30-34: 38 + 12 = 50 The 25th and 26th terms are in the group 20-24, so the median is: Median = (23 + 24) / 2 = 23.5 Next, we need to find the upper quartile, which is the value separating the upper 25% of the data from the lower 75%. We can use the formula: Upper quartile = ((3 * n) + 1) / 4)th term Upper quartile = ((3 * 50) + 1) / 4)th term Upper quartile = 38th term Looking at the cumulative frequency distribution, we see that the 38th term is in the group 25-29. Therefore, the upper quartile is in the group 25-29. The correct option is (C).